1) I disable the original extension (the one with the old name)
2) I install and activate the new extension (the one with the new name)
3) And I then delete completely the original extension (the one with the old name)

Not quite. But what you describe sounds very familiar. I think there's an extension out there somewhere that does this. You also might want to have a look at the Posts merging extension which I'm using here to prevent excessive double posts.